Basic properties
Modulus: | \(4608\) | |
Conductor: | \(4608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(384\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.ck
\(\chi_{4608}(13,\cdot)\) \(\chi_{4608}(61,\cdot)\) \(\chi_{4608}(85,\cdot)\) \(\chi_{4608}(133,\cdot)\) \(\chi_{4608}(157,\cdot)\) \(\chi_{4608}(205,\cdot)\) \(\chi_{4608}(229,\cdot)\) \(\chi_{4608}(277,\cdot)\) \(\chi_{4608}(301,\cdot)\) \(\chi_{4608}(349,\cdot)\) \(\chi_{4608}(373,\cdot)\) \(\chi_{4608}(421,\cdot)\) \(\chi_{4608}(445,\cdot)\) \(\chi_{4608}(493,\cdot)\) \(\chi_{4608}(517,\cdot)\) \(\chi_{4608}(565,\cdot)\) \(\chi_{4608}(589,\cdot)\) \(\chi_{4608}(637,\cdot)\) \(\chi_{4608}(661,\cdot)\) \(\chi_{4608}(709,\cdot)\) \(\chi_{4608}(733,\cdot)\) \(\chi_{4608}(781,\cdot)\) \(\chi_{4608}(805,\cdot)\) \(\chi_{4608}(853,\cdot)\) \(\chi_{4608}(877,\cdot)\) \(\chi_{4608}(925,\cdot)\) \(\chi_{4608}(949,\cdot)\) \(\chi_{4608}(997,\cdot)\) \(\chi_{4608}(1021,\cdot)\) \(\chi_{4608}(1069,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{384})$ |
Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((1,e\left(\frac{83}{128}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4608 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{377}{384}\right)\) | \(e\left(\frac{125}{192}\right)\) | \(e\left(\frac{301}{384}\right)\) | \(e\left(\frac{119}{384}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{117}{128}\right)\) | \(e\left(\frac{79}{192}\right)\) | \(e\left(\frac{185}{192}\right)\) | \(e\left(\frac{163}{384}\right)\) | \(e\left(\frac{25}{48}\right)\) |